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int(0)^(pi)(sin2xcos3x)dx=?...

`int_(0)^(pi)(sin2xcos3x)dx=?`

A

`(4)/(5)`

B

`-(4)/(5)`

C

`(5)/(12)`

D

`-(12)/(5)`

Text Solution

Verified by Experts

`2cosAsinB=sin(A+B)-sin(A-B)`
`:.I=(1)/(2)int_(0)^(pi)(sin5x-sinx)dx=(1)/(2)*[(-cos5x)/(5)+cosx]_(0)^(pi)=(-4)/(5)`.
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